Page 179 - A Mind For Numbers: How to Excel at Math and Science

Physicist Richard Feynman’s introductory physics classes were entirely
different. Feynman, a Nobel Prize winner, was an exuberant guy who played the
bongos for fun and talked more like a down-to-earth taxi driver than a pointy-
headed intellectual.
When Feynman was about eleven years old, an off-the-cuff remark had a
transformative impact on him. He remarked to a friend that thinking is nothing
more than talking to yourself inside.

“Oh yeah?” said Feynman’s friend. “Do you know the crazy shape of the
crankshaft in a car?”
“Yeah, what of it?”
“Good. Now tell me: How did you describe it when you were talking to
yourself?”
It was then that Feynman realized that thoughts can be visual as well as

verbal. 2
He later wrote about how, when he was a student, he had struggled to
imagine and visualize concepts such as electromagnetic waves, the invisible
streams of energy that carry everything from sunlight to cell phone signals. He
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had difficulty describing what he saw in his mind’s eye. If even one of the
world’s greatest physicists had trouble imagining how to see some (admittedly
difficult-to-imagine) physical concepts, where does that leave us normal folks?
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We can find encouragement and inspiration in the realm of poetry. Let’s
take a few poetic lines from a song by American singer-songwriter Jonathan
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Coulton, called “Mandelbrot Set,” about a famous mathematician, Benoit
Mandelbrot.

Mandelbrot’s in heaven
He gave us order out of chaos, he gave us hope where there was none
His geometry succeeds where others fail
So if you ever lose your way, a butterfly will flap its wings
From a million miles away, a little miracle will come to take you home

The essence of Mandelbrot’s extraordinary mathematics is captured in Coulton’s
emotionally resonant phrases, which form images that we can see in our own
mind’s eye—the gentle flap of a butterfly’s wings that spreads and has effects

even a million miles away.
Mandelbrot’s work in creating a new geometry allowed us to understand that
sometimes, things that look rough and messy—like clouds and shorelines—have
a degree of order to them. Visual complexity can be created from simple rules, as